You are correct about it being a bumper automatic, probably a cal. 342 or 344.
http://www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&&2uswk&Omega_342
Your watch most likely has a US made case mated to an Omega swiss movement. Any idea of the case metal? Is it solid 14K or gold-filled?
The band is aftermarket, but looks like it was made about the same era as the watch in the early 1950's.
Hope this helps,
gatorcpa
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